For Over-Dispersed Data
Poisson regression
Poisson regression is the most popular method for modeling count data. The Poisson distribution brings with it the assumption of equi-dispersion that is often unsatisfied.
Almost any real world count data is subject to the possibility of over-dispersion.
\[ f(Y = y) = \frac{\lambda(\lambda + \theta y)^{y-1} e^{-(\lambda + \theta y)}}{y!}, \quad \lambda > 0,\space \theta \in \mathbb{R} \]
| \(\theta = 0\) | \(\theta > 0\) | \(\theta < 0\) |
|---|---|---|
| reduces to Poisson | Models overdispersion | Models underdispersion |
Model | Poisson | NB | GP |
|---|---|---|---|
DIC | 1,291.8 | 1,273.9 | 1,265.6 |
Model | Poisson | NB | CMP |
|---|---|---|---|
DIC | 1,362.39 | 1,350.67 | 1,348.87 |
Model | CMP | Poisson | Neg-Bin |
|---|---|---|---|
AIC | 5,073 | 5,589 | 5,077 |
Nathen Byford